Given any 5 distinct points on the surface of a sphere, show that we can find a closed hemisphere which contains at least 4 of them.
Solution
Pigeonhole principle.
Take a great circle through two of the points. Then at least two of the other three points must lie in one of the hemispheres bounded by the great circle.
© John Scholes
jscholes@kalva.demon.co.uk
11 Dec 2002